A review of geodesics and Busemann G-spaces is given. Aleksandrov curvature and the disjoint (0, n)-cells property are defined. We show how these properties are applied to and strengthened in Busemann G-spaces. We examine the relationship between manifolds and Busemann G-spaces and prove that all Riemannian manifolds are Busemann G-spaces, though not all metric manifolds are Busemann G-spaces. We show how Busemann G-spaces that also have bounded Aleksandrov curvature admit local closest-point projections to geodesic segments. Finally, we expound local properties of Busemann G-spaces and define a new property which we call the symmetric property. We show that Busemann G-spaces which have the disjoint (0,n)-cells property for every value of n cannot have the symmetric property.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Safsten, Clarke Alexander, "Busemann G-Spaces, CAT(k) Curvature, and the Disjoint (0, n)-Cells Property" (2017). All Theses and Dissertations. 6486.
Busemann, geodesic, disjoint (0, n)-cells, Aleksandrov curvature